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Orthogonal Procrustes Analysis: Its Transformation Arrangement and Minimal Distance

Toni Bakhtiar, Siswadi

Abstract


Procrustes analysis theory is a set of mathematical least-squares tools to directly estimate and perform simultaneous similarity transformations among the model point coordinates matrices up to their maximal agreement. Typically, Procrustes analysis employs a series of linear transformation, i.e., translation, rotation, and dilation to best match one configuration to the other. The primary objective of this paper is to provide a mathematical verification on how such kind of transformation ordering can perform a minimum difference measurement between configurations. With three linear transformations precede the process, we have six different transformation orderings. We then carry-out a direct comparison toward the sum of the squared distance obtained from different ordering. It is proved that a series of transformation in the standard command, i.e., translation-rotation-dilation, provides the lowest possible Procrustes distance.

Keywords


Procrustes analysis, transformation ordering, translation, rotation, dilation.

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